/export/starexec/sandbox/solver/bin/starexec_run_standard /export/starexec/sandbox/benchmark/theBenchmark.hs /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES proof of /export/starexec/sandbox/benchmark/theBenchmark.hs # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty H-Termination with start terms of the given HASKELL could be proven: (0) HASKELL (1) BR [EQUIVALENT, 0 ms] (2) HASKELL (3) COR [EQUIVALENT, 0 ms] (4) HASKELL (5) Narrow [SOUND, 0 ms] (6) AND (7) QDP (8) QDPSizeChangeProof [EQUIVALENT, 0 ms] (9) YES (10) QDP (11) QDPSizeChangeProof [EQUIVALENT, 0 ms] (12) YES ---------------------------------------- (0) Obligation: mainModule Main module Main where { import qualified Prelude; } ---------------------------------------- (1) BR (EQUIVALENT) Replaced joker patterns by fresh variables and removed binding patterns. ---------------------------------------- (2) Obligation: mainModule Main module Main where { import qualified Prelude; } ---------------------------------------- (3) COR (EQUIVALENT) Cond Reductions: The following Function with conditions "undefined |Falseundefined; " is transformed to "undefined = undefined1; " "undefined0 True = undefined; " "undefined1 = undefined0 False; " ---------------------------------------- (4) Obligation: mainModule Main module Main where { import qualified Prelude; } ---------------------------------------- (5) Narrow (SOUND) Haskell To QDPs digraph dp_graph { node [outthreshold=100, inthreshold=100];1[label="notElem",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3]; 3[label="notElem vx3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3]; 4[label="notElem vx3 vx4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3]; 5[label="all . (/=)",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3]; 6[label="all ((/=) vx3) vx4",fontsize=16,color="black",shape="box"];6 -> 7[label="",style="solid", color="black", weight=3]; 7[label="and . map ((/=) vx3)",fontsize=16,color="black",shape="box"];7 -> 8[label="",style="solid", color="black", weight=3]; 8[label="and (map ((/=) vx3) vx4)",fontsize=16,color="black",shape="box"];8 -> 9[label="",style="solid", color="black", weight=3]; 9[label="foldr (&&) True (map ((/=) vx3) vx4)",fontsize=16,color="burlywood",shape="triangle"];40[label="vx4/vx40 : vx41",fontsize=10,color="white",style="solid",shape="box"];9 -> 40[label="",style="solid", color="burlywood", weight=9]; 40 -> 10[label="",style="solid", color="burlywood", weight=3]; 41[label="vx4/[]",fontsize=10,color="white",style="solid",shape="box"];9 -> 41[label="",style="solid", color="burlywood", weight=9]; 41 -> 11[label="",style="solid", color="burlywood", weight=3]; 10[label="foldr (&&) True (map ((/=) vx3) (vx40 : vx41))",fontsize=16,color="black",shape="box"];10 -> 12[label="",style="solid", color="black", weight=3]; 11[label="foldr (&&) True (map ((/=) vx3) [])",fontsize=16,color="black",shape="box"];11 -> 13[label="",style="solid", color="black", weight=3]; 12[label="foldr (&&) True (((/=) vx3 vx40) : map ((/=) vx3) vx41)",fontsize=16,color="black",shape="box"];12 -> 14[label="",style="solid", color="black", weight=3]; 13[label="foldr (&&) True []",fontsize=16,color="black",shape="box"];13 -> 15[label="",style="solid", color="black", weight=3]; 14 -> 16[label="",style="dashed", color="red", weight=0]; 14[label="(&&) (/=) vx3 vx40 foldr (&&) True (map ((/=) vx3) vx41)",fontsize=16,color="magenta"];14 -> 17[label="",style="dashed", color="magenta", weight=3]; 15[label="True",fontsize=16,color="green",shape="box"];17 -> 9[label="",style="dashed", color="red", weight=0]; 17[label="foldr (&&) True (map ((/=) vx3) vx41)",fontsize=16,color="magenta"];17 -> 18[label="",style="dashed", color="magenta", weight=3]; 16[label="(&&) (/=) vx3 vx40 vx5",fontsize=16,color="black",shape="triangle"];16 -> 19[label="",style="solid", color="black", weight=3]; 18[label="vx41",fontsize=16,color="green",shape="box"];19[label="(&&) not (vx3 == vx40) vx5",fontsize=16,color="black",shape="box"];19 -> 20[label="",style="solid", color="black", weight=3]; 20[label="(&&) not (primEqChar vx3 vx40) vx5",fontsize=16,color="burlywood",shape="box"];42[label="vx3/Char vx30",fontsize=10,color="white",style="solid",shape="box"];20 -> 42[label="",style="solid", color="burlywood", weight=9]; 42 -> 21[label="",style="solid", color="burlywood", weight=3]; 21[label="(&&) not (primEqChar (Char vx30) vx40) vx5",fontsize=16,color="burlywood",shape="box"];43[label="vx40/Char vx400",fontsize=10,color="white",style="solid",shape="box"];21 -> 43[label="",style="solid", color="burlywood", weight=9]; 43 -> 22[label="",style="solid", color="burlywood", weight=3]; 22[label="(&&) not (primEqChar (Char vx30) (Char vx400)) vx5",fontsize=16,color="black",shape="box"];22 -> 23[label="",style="solid", color="black", weight=3]; 23[label="(&&) not (primEqNat vx30 vx400) vx5",fontsize=16,color="burlywood",shape="triangle"];44[label="vx30/Succ vx300",fontsize=10,color="white",style="solid",shape="box"];23 -> 44[label="",style="solid", color="burlywood", weight=9]; 44 -> 24[label="",style="solid", color="burlywood", weight=3]; 45[label="vx30/Zero",fontsize=10,color="white",style="solid",shape="box"];23 -> 45[label="",style="solid", color="burlywood", weight=9]; 45 -> 25[label="",style="solid", color="burlywood", weight=3]; 24[label="(&&) not (primEqNat (Succ vx300) vx400) vx5",fontsize=16,color="burlywood",shape="box"];46[label="vx400/Succ vx4000",fontsize=10,color="white",style="solid",shape="box"];24 -> 46[label="",style="solid", color="burlywood", weight=9]; 46 -> 26[label="",style="solid", color="burlywood", weight=3]; 47[label="vx400/Zero",fontsize=10,color="white",style="solid",shape="box"];24 -> 47[label="",style="solid", color="burlywood", weight=9]; 47 -> 27[label="",style="solid", color="burlywood", weight=3]; 25[label="(&&) not (primEqNat Zero vx400) vx5",fontsize=16,color="burlywood",shape="box"];48[label="vx400/Succ vx4000",fontsize=10,color="white",style="solid",shape="box"];25 -> 48[label="",style="solid", color="burlywood", weight=9]; 48 -> 28[label="",style="solid", color="burlywood", weight=3]; 49[label="vx400/Zero",fontsize=10,color="white",style="solid",shape="box"];25 -> 49[label="",style="solid", color="burlywood", weight=9]; 49 -> 29[label="",style="solid", color="burlywood", weight=3]; 26[label="(&&) not (primEqNat (Succ vx300) (Succ vx4000)) vx5",fontsize=16,color="black",shape="box"];26 -> 30[label="",style="solid", color="black", weight=3]; 27[label="(&&) not (primEqNat (Succ vx300) Zero) vx5",fontsize=16,color="black",shape="box"];27 -> 31[label="",style="solid", color="black", weight=3]; 28[label="(&&) not (primEqNat Zero (Succ vx4000)) vx5",fontsize=16,color="black",shape="box"];28 -> 32[label="",style="solid", color="black", weight=3]; 29[label="(&&) not (primEqNat Zero Zero) vx5",fontsize=16,color="black",shape="box"];29 -> 33[label="",style="solid", color="black", weight=3]; 30 -> 23[label="",style="dashed", color="red", weight=0]; 30[label="(&&) not (primEqNat vx300 vx4000) vx5",fontsize=16,color="magenta"];30 -> 34[label="",style="dashed", color="magenta", weight=3]; 30 -> 35[label="",style="dashed", color="magenta", weight=3]; 31[label="(&&) not False vx5",fontsize=16,color="black",shape="triangle"];31 -> 36[label="",style="solid", color="black", weight=3]; 32 -> 31[label="",style="dashed", color="red", weight=0]; 32[label="(&&) not False vx5",fontsize=16,color="magenta"];33[label="(&&) not True vx5",fontsize=16,color="black",shape="box"];33 -> 37[label="",style="solid", color="black", weight=3]; 34[label="vx4000",fontsize=16,color="green",shape="box"];35[label="vx300",fontsize=16,color="green",shape="box"];36[label="(&&) True vx5",fontsize=16,color="black",shape="box"];36 -> 38[label="",style="solid", color="black", weight=3]; 37[label="(&&) False vx5",fontsize=16,color="black",shape="box"];37 -> 39[label="",style="solid", color="black", weight=3]; 38[label="vx5",fontsize=16,color="green",shape="box"];39[label="False",fontsize=16,color="green",shape="box"];} ---------------------------------------- (6) Complex Obligation (AND) ---------------------------------------- (7) Obligation: Q DP problem: The TRS P consists of the following rules: new_foldr(vx3, :(vx40, vx41)) -> new_foldr(vx3, vx41) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (8) QDPSizeChangeProof (EQUIVALENT) By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. From the DPs we obtained the following set of size-change graphs: *new_foldr(vx3, :(vx40, vx41)) -> new_foldr(vx3, vx41) The graph contains the following edges 1 >= 1, 2 > 2 ---------------------------------------- (9) YES ---------------------------------------- (10) Obligation: Q DP problem: The TRS P consists of the following rules: new_asAs(Succ(vx300), Succ(vx4000), vx5) -> new_asAs(vx300, vx4000, vx5) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (11) QDPSizeChangeProof (EQUIVALENT) By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. From the DPs we obtained the following set of size-change graphs: *new_asAs(Succ(vx300), Succ(vx4000), vx5) -> new_asAs(vx300, vx4000, vx5) The graph contains the following edges 1 > 1, 2 > 2, 3 >= 3 ---------------------------------------- (12) YES